Gap junctions destroy persistent states in excitatory networks

Gap junctions between excitatory neurons are shown to disrupt the persistent state. The asynchronous state of the network loses stability via a Hopf bifurcation and then the active state is destroyed via a homoclinic bifurcation with a stationary state. A partial differential equation (PDE) is developed to analyze the Hopf and the homoclinic bifurcations. The simplified dynamics are compared to a biophysical model where similar behavior is observed. In the low noise case, the dynamics of the PDE is shown to be very complicated and includes possible chaotic behavior. The onset of synchrony is studied by the application of averaging to obtain a simple criterion for destabilization of the asynchronous persistent state.